The impact of elastohydrodynamic lubrication on the time-varying meshing stiffness of planetary gear-annulus pair

This study proposes a novel method for calculating the time-varying mesh stiffness (TVMS) of a planetary gear-annulus pair considering elastohydrodynamic lubrication (EHL) to investigate the impact of EHL characteristics between gear surfaces on the mesh stiffness in planetary transmission systems. First, based on the contact performance of gear pairs under EHL, a mesh model and an EHL model for planetary gear-annulus pairs were established. The relationships between the relative sliding velocity, relative curvature radius, and roll-absorbing speed during gear meshing were established. Additionally, a generalised Reynolds equation and load equation were formulated based on the relationship between pressure, lubricant viscosity, and density, allowing for an analysis of the effects of the roll-absorbing speed and load torque on the oil film pressure and thickness between the gear surfaces. Second, the local slope method was employed to solve for the oil film stiffness between the gear surfaces, and a contact stiffness model of the planetary gear-annulus pair, incorporating the oil film stiffness, was established using the slicing method. The TVMS of the planetary gear-annulus pair was then solved using the potential energy method based on the obtained oil film pressure and thickness values, as follows: Compared with traditional potential energy methods, this approach improved the accuracy of the TVMS calculations for a planetary gear-annulus pair. Finally, the effects of different entrainment velocities and load torque on the TVMS were assessed. The results showed that as the roll-absorbing speed increased, the TVMS decreased, whereas an increase in the load torque led to an increase in TVMS.